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 A316707 For any n >= 0 with base-5 expansion Sum_{k=0..w} d_k * 5^k, let f(n) = Sum_{k=0..w} [d_k > 0] * (2 + i)^k * i^(d_k - 1) (where [] is an Iverson bracket and i denotes the imaginary unit); a(n) equals the square of the modulus of f(n). 2
 0, 1, 1, 1, 1, 5, 10, 8, 2, 4, 5, 4, 10, 8, 2, 5, 2, 4, 10, 8, 5, 8, 2, 4, 10, 25, 32, 34, 20, 18, 50, 61, 61, 41, 41, 40, 45, 53, 37, 29, 10, 13, 17, 9, 5, 20, 29, 25, 13, 17, 25, 18, 32, 34, 20, 20, 17, 29, 25, 13, 50, 41, 61, 61, 41, 40, 29, 45, 53, 37, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS See A316657 for the real part of f and additional comments. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A316657(n)^2 + A316658(n)^2. a(5 * n) = 5 * a(n) for any n >= 0. a(5^k) = 5^k for any k >= 0. PROG (PARI) a(n) = my (d=Vecrev(digits(n, 5)), z=sum(i=1, #d, if (d[i], (2+I)^(i-1) * I^(d[i]-1), 0))); real(z)^2 + imag(z)^2 CROSSREFS Cf. A316657, A316658. Sequence in context: A067843 A245942 A280943 * A109360 A141622 A144136 Adjacent sequences: A316704 A316705 A316706 * A316708 A316709 A316710 KEYWORD nonn,base AUTHOR Rémy Sigrist, Jul 11 2018 STATUS approved

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Last modified December 3 01:25 EST 2022. Contains 358510 sequences. (Running on oeis4.)